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Gabbasov, N. S.; Zamaliev, R. R.

A new variant of the subdomain method for integral equations of the third kind with singularities in the kernel. (English. Russian original) Zbl 1232.45007

Russ. Math. 55, No. 5, 8-13 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2011, No. 5, 12-18 (2011).
The authors study integral equations of the third kind with fixed singularities in the kernel. The integral is understood in the sense of the Hadamard finite part. They construct a new variant of the subdomain method for the approximate solution in the space of generalized functions. They prove the unique solvability of the corresponding approximate equation, estimate the error of the approximate solution and prove the convergence of a sequence of approximate solutions to the exact one. The stability and well-posedness of the approximating equations are also studied.
Reviewer: Adrian Carabineanu (Bucureşti)

Cited in 7 Documents

MSC:

45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
45L05 Theoretical approximation of solutions to integral equations

Keywords:

integral equations of the third kind; space of generalized functions; approximate solution; subdomain method; theoretical justification; error estimate
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References:

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[11] N. S. Gabbasov and R. R. Zamaliev, ”An Integral Equation of the Third Kind with Fixed Singularities in the Kernel,” in Proceedings of the Republican Scientific-Practical Conference ”Science, Technologies, and Communications in Modern Society ” (Naberezhnye Chelny, 2009), Vol. 2, pp. 41–44.
[12] N. S. Gabbasov and R. R. Zamaliev, ”A Generalized Solution of an Integral Equation of the Third Kind with Fixed Singularities in the Kernel,” in Trudy Matem. Tsentra im. N. I. Lobachevskogo (Kazansk. Matem. Ob-vo, Kazan, 2009), Vol. 38, pp. 76–79.
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